Justice Ginsburg said the chief justice’s “life experience” had played a part in the shift. One of his daughters was a recently divorced mother with a demanding job.

Justice Ginsburg’s explanation in 2009, though widely accepted, was but informed speculation. Now there is data to go with the intuition.

It turns out that judges with daughters are more likely to vote in favor of women’s rights than ones with only sons. The effect, a new study found, is most pronounced among male judges appointed by Republican presidents, like Chief Justice Rehnquist.

“Our basic finding is quite startling,” said Maya Sen, a political scientist at the University of Rochester who conducted the study along with Adam Glynn, a government professor at Harvard.

The standard scholarly debate about how judges decide cases tends to revolve around two factors: law and ideology. “Here, we’ve found evidence that there is a third factor that matters: personal experiences,” Professor Sen said. “Things like having daughters can actually fundamentally change how people view the world, and this, in turn, affects how they decide cases.”

The new study considered about 2,500 votes by 224 federal appeals court judges. “Having at least one daughter,” it concluded, “corresponds to a 7 percent increase in the proportion of cases in which a judge will vote in a feminist direction.”

Additional daughters do not seem to matter. But the effect of having a daughter is even larger when you limit the comparison to judges with only one child.

“Having one daughter as opposed to one son,” the study found, “is linked to an even higher 16 percent increase in the proportion of gender-related cases decided in a feminist direction.”

The authors also looked at the same judges’ votes in a separate set of 3,000 randomly chosen cases. There was no relationship between having daughters and liberal votes generally. Daughters made a difference in only “civil cases having a gendered dimension.”

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Chief Justice William H. Rehnquist in 2005 with his daughter Janet, who was said to have informed his decision-making.CreditJ. Scott Applewhite/Associated Press

Researchers have found similar “daughter effects” in other areas. Members of Congress with daughters are more likely to cast liberal votes, particularly on abortion rights, one study found. Another study showed that British parents with daughters were more likely to vote for left-wing parties, while ones with sons were more likely to vote for right-wing parties.

The new study on judges considered some possible explanations. Perhaps judges wanted to shield their daughters from harm. But the voting trends showed up in only civil cases, like ones involving claims of employment discrimination, and not criminal ones, including rape and sexual assault.

Or perhaps daughters tend to be liberal and succeed in lobbying their parents to vote in a liberal direction. But the judicial voting trends were limited to civil cases in which gender played a role.

The study was lukewarm about the possibility that judges acted out of economic self-interest — to avoid, say, having unemployed daughters.

The most likely explanation, Professor Sen said, was the one offered by Justice Ginsburg. “By having at least one daughter,” Professor Sen said, “judges learn about what it’s like to be a woman, perhaps a young woman, who might have to deal with issues like equity in terms of pay, university admissions or taking care of children.”

In the 2003 decision that so delighted Justice Ginsburg, Nevada Department of Human Resources v. Hibbs, the Supreme Court considered whether workers could sue state employers for violating a federal law that allowed time off for family emergencies. Chief Justice Rehnquist, who had long championed states’ rights, had not been expected to be sympathetic to the idea.

Instead, he wrote the majority opinion sustaining the law. It was, he said, meant to address “the pervasive sex-role stereotype that caring for family members is women’s work.”

Chief Justice Rehnquist was 78 when he wrote that. He died a couple of years later, in 2005. In the term he wrote the opinion, he sometimes left work early to pick up his granddaughters from school.

“When his daughter Janet was divorced,” Justice Ginsburg told Emily Bazelon in the 2009 interview in The New York Times, “I think the chief felt some kind of responsibility to be kind of a father figure to those girls. So he became more sensitive to things that he might not have noticed.”

I asked Professor Sen what her study suggested about how to think about the Supreme Court.

“Justices and judges aren’t machines,” she said. “They are human, just like you and me. And just like you and me, they have personal experiences that affect how they view the world.

“Having daughters,” she said, “is just one kind of personal experience, but there could be other things — for example, serving in the military, adopting a child or seeing a law clerk come out as gay. All of these things could affect a justice’s worldview.”

A version of this article appears in print on , on Page A14 of the New York edition with the headline: Another Factor Said to Sway Judges to Rule for Women’s Rights: A Daughter. Order Reprints | Today’s Paper | Subscribe